MCMC based simulation methodology for reliability calculations

This paper presents a methodology for general nonlinear reliability problems. It is based on dividing the failure domain into a number of appropriately selected subregions and calculating the failure probability as a sum of the probabilities associated with each of these subregions. The probability of each subregion is calculated as a product of factors. These factors can be estimated quite accurately by a relatively small number of samples generated according to the conditional distribution of different subregions. The generation of such samples is achieved through Markov Chain Monte Carlo (MCMC) simulations using a slice-sampling-based algorithm proposed by the authors. This algorithm overcomes difficulties in choosing an appropriate proposal sampling density encountered by other MCMC algorithms, such as the Metropolis-Hastings algorithm. The proposed method is very robust and is suitable for treating high-dimensional problems, say involving hundreds or thousands of random parameters. This is in contrast to popular importance sampling methods that often break down when one moves to high-dimensional problems. The method is found to be significantly more efficient than Monte Carlo simulations (MCS). The reduction in computational effort over MCS increases as one deals with problems involving smaller failure probability. The method is demonstrated with a numerical example involving 3000 random variables.